Question

-.At a fair hamburgers sell for $3.00 each and hot dogs sell for $1.50 each. The equation 3x + 1.5y = 30 describes the number of hamburgers and hot dog a family can buy with $30 a. b.

Answer 1

Part a) The y-intercept is the point (0,20) and the x-intercept is the point (10,0)

The graph in the attached figure

Part b) See the procedure

Explanation:

The questions are

Part a) Find the intercepts and graph the function

Part b) What does each intercept represent?

Part a) Find the intercepts and graph the function

Let

x-----> the number of hamburgers

y ----> the number of hot dogs

we have

`3x+1.5y=30`

Remember that

The y-intercept is the value of y when the value of x is equal to zero

so

For x=0

`3(0)+1.5y=30`

`1.5y=30`

`y=20\ hot\ dogs`

The y-intercept is the point (0,20)

The x-intercept is the value of x when the value of y is equal to zero

so

For y=0

`3x+1.5(0)=30`

`3x=30`

`x=10\ hamburgers`

The x-intercept is the point (10,0)

Plot the intercepts and graph the line

see the attached figure

Part b) What does each intercept represent?

The x-intercept is the number of hamburgers they can buy if they buy no hot dogs

The y-intercept is the number of hot dogs they can buy if they buy no hamburgers